It is common today to provide navigational map displays of the landscape or seascape over which a vehicle is passing, with the vehicle's current position indicated thereon. These displays are almost always flat, which requires that the curved surface of the earth be presented in two dimensions rather than its actual three dimensions. The curvature of the earth is not ignored, rather the curved surface of the earth is projected onto a two-dimensional plane and that projection is what is presented on the display.
FIG. 1 illustrates graphically method 20 of generating two dimensional equidistant cylindrical map projection (ECP) 22 of a spherical surface (e.g., the three dimensional earth's surface) 24 and the distortion inherent in such a projection. Consider spherical surface 24 located within tangential cylindrical surface 22. Vector 26 makes latitude angle Φ and longitude angle λ with respect to the axes of spherical surface 24. Vector 26 intersects spherical surface 24 at location 28 (Φ,λ) and surrounding cylindrical surface 22 at location 30 (y,x). Cylindrical surface 22 is unwrapped and flattened as shown by two dimensional surface 22-1 at the right of FIG. 1. Horizontal lines 34 on cylindrical surface 22-1 correspond to latitude lines on spherical surface 24 and vertical lines 32 on cylindrical surface 22-1 correspond to longitude lines on spherical surface 24. There is a one-to-one correspondence between (Φ,λ) on spherical surface 24 and (y,x) on cylindrical surface 22 and 22-1. Assuming that the center of projection is the equator and any one meridian along the equator, a consequence of this cylindrical projection is that the cylindrical map display is stretched toward the poles (Φ=±π/2). However, there is no distortion along any meridian and the equator is the only parallel that does not have any distortion. The distortion along any parallel is given by k=cosine(Φ1)/cosine(Φ), where Φ1 is the latitude of the center of projection. Stated another way, the map scale varies with position on the map display so that the magnitude of these distortions change depending upon the distance of observation from the center of projection. For example, two mountain peaks will appear to have a first separation when located a first distance from an observer and a different separation when located at a second distance from the observer assuming that the center of projection has changed along with the observer. This relative location error can make safe and precise navigation more difficult.
In a navigational display, the current position of a vehicle or observer in the vehicle is plotted on a two-dimensional map display and updated as the vehicle moves. The map may remain fixed while the vehicle position appears to move across the fixed map display or the vehicle position can remain fixed on the display and the map appears to move under the vehicle. Either arrangement is common. While the above noted distortion problem associated with flat navigational displays applies to any type of moving vehicle (e.g., car, ship, plane, etc.) or observer therein, they are more apparent with aircraft because of the aircraft's relatively high speed. The larger the distance that the aircraft travels over the surface of the earth per unit time, the less time the pilot has to take into account the inherent distortions of the map display and select a safe flight path. Accordingly, it is desirable to provide an aircraft map display on which the aircraft position relative to map features is presented in such a way that the directions and relative distances between the aircraft and any map features are accurately presented. In addition, it is desirable that these directions and distances be independent of the aircraft location relative to a particular feature on the map display. Thus, the pilot or navigator can evaluate at a glance the direction and relative distance between his or her aircraft and a potential navigation hazard without concern for map distortions inherent in the two-dimensional presentation of the curved surface of the earth. In addition, it is desirable that the display of the local area map and aircraft position be automatically updated in a manner that preserves this intuitive direction and distance visualization accuracy. Furthermore, other desirable features and characteristics of the present invention will become apparent from the subsequent detailed description of the invention and the appended claims, taken in conjunction with the accompanying drawings and this background of the invention.